Book cover for Thermodynamics: An Engineering Approach

Thermodynamics: An Engineering Approach

Yunus A. Cengel, Michael A. Boles

ISBN #9781259822674

9th Edition

2,694 Questions

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Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter delves into the fundamental principles of chemical and phase equilibrium, emphasizing how the minimization of Gibbs free energy and the maximization of entropy drive systems to equilibrium. Key thermodynamic tools such as equilibrium constants, the Gibbs phase rule, Raoult’s law, and Henry’s law are discussed, along with practical considerations in combustion processes, steady-flow versus closed systems, and specialized applications like fuel cells. A strong understanding of these concepts is essential for analyzing and optimizing chemical reactions in various practical and industrial scenarios.

Learning Objectives

1

Explain the principles of chemical equilibrium and phase equilibrium, including the roles of Gibbs free energy minimization and entropy maximization.

2

Define and apply equilibrium constants and key thermodynamic laws such as the Gibbs phase rule, Raoult’s law, and Henry’s law.

3

Analyze the differences between theoretical and actual combustion processes in both steady-flow and closed systems.

4

Evaluate how adiabatic flame temperatures, entropy changes, and second-law analyses contribute to understanding reacting systems.

5

Examine the functioning of fuel cells as a special application of chemical and phase equilibrium.

Key Concepts

CONCEPT

DEFINITION

Chemical Equilibrium

The state of a reacting system where the Gibbs free energy is minimized (or, equivalently, the entropy is maximized in an isolated system), meaning no net change in the concentrations of reactants and products.

Phase Equilibrium

A condition where the chemical potential of each component is uniform across all phases, ensuring balanced mass transfer between phases.

Gibbs Free Energy (G)

A thermodynamic potential that indicates the maximum reversible work obtainable from a system at constant temperature and pressure; a system at equilibrium will have minimized G.

Equilibrium Constant (K)

A numerical value that expresses the ratio of the product concentrations to the reactant concentrations at equilibrium, indicating the position of equilibrium.

Gibbs Phase Rule

A principle that provides the number of degrees of freedom (variables) in a phase equilibrium system based on the number of components and phases present.

Raoult’s Law

A law that relates the vapor pressure of a component in an ideal solution to its mole fraction; used to analyze vapor-liquid equilibria.

Henry’s Law

A law that relates the solubility of a gas in a liquid to the partial pressure of that gas above the solution.

Adiabatic Flame Temperature

The maximum temperature reached by the products of combustion in an adiabatic process (no heat loss to the environment).

Steady-Flow Systems

Systems in which mass and energy flow are continuous and constant over time.

Closed Systems

Systems where no mass is exchanged with the surroundings, though energy exchange may occur.

Second-Law Analysis

An analysis approach based on the second law of thermodynamics, focusing on energy dispersal and entropy changes during chemical reactions.

Example Problems

Example 1

What are the approximate chemical compositions of gasoline, diesel fuel, and natural gas?

Example 2

How does the presence of $\mathrm{N}_{2}$ in air affect the outcome of a combustion process?

Example 3

Is the number of atoms of each element conserved during a chemical reaction? How about the total number of moles?

Example 4

What is the air-fuel ratio? How is it related to the fuel-air ratio?

Example 5

Is the air-fuel ratio expressed on a mole basis identical to the air-fuel ratio expressed on a mass basis?
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Step-by-Step Explanations

QUESTION

Why does a reacting system reach chemical equilibrium when Gibbs free energy is minimized?

STEP-BY-STEP ANSWER:

Step 1: Recognize that Gibbs free energy (G) is a measure of the useful energy available in a system at constant temperature and pressure.
Step 2: Understand that for a spontaneous process, the change in G (ΔG) must be negative, indicating that the system is moving toward a lower energy state.
Step 3: At the point where G is at a minimum, the system has no driving force to change further, meaning the forward and reverse reactions occur at the same rate.
Step 4: This state of no net change in energy and composition defines chemical equilibrium.
Final Answer: Chemical equilibrium is achieved when the system’s Gibbs free energy is minimized because at that point, no further net reaction can occur without energy input.

Chemical Equilibrium (Gibbs Free Energy Minimization)

QUESTION

How does uniform chemical potential across phases ensure phase equilibrium?

STEP-BY-STEP ANSWER:

Step 1: Define chemical potential as the partial molar free energy of a component in a given phase.
Step 2: Recognize that if the chemical potential is not equal between phases, there will be a net transfer of the component from one phase to the other.
Step 3: Equilibrium is reached when the chemical potential of each component is identical across all phases, meaning no net migration of species occurs.
Final Answer: Phase equilibrium is maintained because uniform chemical potential prevents further mass transfer between phases.

Phase Equilibrium (Uniform Chemical Potential)

QUESTION

How can the equilibrium constant (K) be derived from the conditions of chemical equilibrium?

STEP-BY-STEP ANSWER:

Step 1: Start with the reaction’s balanced chemical equation.
Step 2: Apply the law of mass action to express K as the ratio of products raised to their stoichiometric coefficients to reactants raised to theirs.
Step 3: Relate the change in Gibbs free energy (ΔG) to K through the equation ΔG = -RT ln(K), where R is the gas constant and T is the temperature.
Step 4: At equilibrium, ΔG is zero, which allows calculation of K for any given reaction.
Final Answer: The equilibrium constant K is derived by linking the reaction quotient to the Gibbs free energy change, leading to the relation ΔG = -RT ln(K) at equilibrium.

Equilibrium Constant (K)

QUESTION

How is Raoult's law used to analyze vapor-liquid equilibrium in ideal solutions?

STEP-BY-STEP ANSWER:

Step 1: Write the expression for Raoult’s law which relates the partial vapor pressure of a component to its mole fraction in the liquid phase.
Step 2: Understand that in an ideal solution, the total vapor pressure is the sum of the individual partial pressures.
Step 3: Use the law to calculate the vapor pressures of each component and predict the composition of the vapor phase.
Final Answer: Raoult’s law assists in predicting the behavior of components in a vapor-liquid equilibrium by relating their partial pressures to mole fractions.

Application of Raoult’s Law

QUESTION

How does second-law analysis aid in understanding reacting systems?

STEP-BY-STEP ANSWER:

Step 1: Recall that the second law of thermodynamics deals with the direction of energy dispersal and the increase of entropy.
Step 2: Analyze how a reacting system approaches equilibrium by maximizing entropy, especially in isolated systems.
Step 3: Evaluate the efficiencies and feasibility of reactions by considering energy losses and irreversibility.
Final Answer: Second-law analysis simplifies the evaluation of reacting systems by emphasizing entropy changes and the inherent irreversibility of real processes.

Second-Law Analysis in Reacting Systems

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Common Mistakes

  • Confusing chemical equilibrium with phase equilibrium, despite their distinct conditions.
  • Assuming that the minimization of Gibbs free energy applies identically to all systems without considering system constraints (e.g., steady-flow vs. closed systems).
  • Overlooking the specific conditions under which Raoult’s law and Henry’s law are applicable, leading to misinterpretation of vapor-liquid equilibria.
  • Neglecting the impact of temperature and pressure on both equilibrium constants and adiabatic flame temperatures.
  • Mixing up the concepts of theoretical combustion processes with actual combustion behavior without accounting for real-world inefficiencies.